Method for frequency tuning of a micro-mechanical resonator

ABSTRACT

A method for modifying the resonance frequency of a micro-mechanical resonator, and resonators on which the method is practiced. A packaged resonator is trimmed by directing electromagnetic energy to the resonator through a transparent portion of the package. The removal of mass (by the energy) affects the resonance frequency of the resonator in a predictable manner. In some embodiments, the energy is sourced from a femtosecond laser. In some variations of the illustrative embodiment, the amount of mass to be removed is determined as a function of its location on the resonator. A mass-trimming map is developed that identifies a plurality of potential mass-trimming sites on the resonator. A site can be classified as a fine-tuning site or a coarse-tuning site as a function of the degree to which mass removal at those sites affects the resonance frequency. The sites can also be characterized as a function of their position relative to features of the resonator (e.g., nodal lines, etc.). Based on a differential between the measured and desired resonance frequency of the resonator, and expressions that relate resonance frequency to location-dependent mass, actual sites for mass removal are selected from among of the plurality of potential mass-trimming sites.

FIELD OF THE INVENTION

The present invention relates to micro-electromechanical systems(“MEMS”), and, more particularly, to frequency trimming of MEMSresonators.

BACKGROUND OF THE INVENTION

MEMS resonators are now being developed for use in frequency-specificapplications, such as oscillator references and highly-selectivebandpass filters. These applications require that the resonator possessa specific resonance frequency. For example, in the case of anoscillator that serves as part of a clock circuit, it is important thatthe resonator vibrates at a specific frequency. In the case of a filter,a resonator must likewise vibrate at a particular, targeted frequency togenerated passband to selectively pass or reject a signal as a functionof frequency.

Due to the vagaries of manufacturing, the measured resonance frequencyof a resonator is typically different from its targeted value.Variations of about 5 percent are typical. As a consequence, anewly-manufactured resonator often needs to be tuned to adjust itsresonance frequency. Tuning of a resonator is akin to tuning a piano,although the techniques used are quite different. The process of tuninga resonator is called “trimming.”

Frequency trimming is well-known. Indeed, it is commonplace to trim theresonance frequency of piezo-electric components (e.g., crystals, etc.),and resonators, oscillators, and clocks that incorporate them.Unfortunately, the techniques that are used for frequency trimming thesedevices are not well adapted for use with MEMS resonators.

For example, laser trimming has traditionally been used to trim theresonance frequency of crystals. But laser trimming has not beenconsidered to be a viable technique for use with MEMS resonators sincethey are typically much smaller in size than their crystal counterparts.Also, it is desirable to trim a MEMS resonator after it has beenpackaged, but doing has not been considered to be feasible via laser.(See, e.g., Joachim et al., “Characterization of Selective PolysiliconDeposition for MEMS Resonator Tuning,” J. MEMS, v(12), no. 2, pp.193-200 (April 2003) at p. 193; Lin et al., “MicroelectromechanicalFilters for Signal Processing,” J. MEMS, v(7), no. 3, pp. 286-294 (Sept.1998) at p. 293; U.S. Pat. Nos. 6,600,389 at col. 1, lines 33-39, and6,570,468 at col. 1, lines 27-34).

Other techniques that have been used to trim piezo-electric componentsinclude removing mass by polishing or adding mass by depositing a resin(see, e.g., U.S. Pat. No. 6,604,266 at col. 1, lines 20-49). Thesetechniques are not well suited for trimming MEMS resonators either. Inparticular, the very small size (micron and even submicron size) of MEMSresonators makes polishing and selective deposition difficult.Furthermore, the spring constant of the resonator is very sensitive tobeam thickness. Variations in the spring constant, such as can be causedby removal or addition of material, will affect the quality factor, Q,of the resonator.

Since frequency-trimming techniques that have been used forpiezo-electric components are not readily adapted for use with a MEMSresonator, new frequency-trimming techniques have been developed.

In a first frequency-trimming technique that is useful with MEMSresonators, the resonance frequency of a resonator is changed bymodifying a structure that supports the resonator. See, U.S. Pat. No.6,570,468. In this technique, the resonance frequency of a resonator isaltered by changing the stiffness of a supporting structure. Accordingto the patent, the stiffness of the supporting structure is modified byforming notches therein or by adding material thereto.

In a second approach to the problem of tuning a MEMS resonator, astructure having a plurality of beams of variable length is formed. See,U.S. Pat. No. 6,600,389. According to this approach, the variation inbeam length results in a difference in resonance frequency between theshortest and longest beam that is sufficient to account for the typicalvariation (due to manufacturing tolerances) in the resonance frequencyof a resonator. This patent also discloses that the increment inresonance frequency between adjacent beams is smaller than the targetedfrequency variation tolerance of the desired resonator. Therefore, oneof the beams will be qualified to serve as the desired resonator. Oncethat beam is identified, the other beams are disabled.

The techniques described in U.S. Pat. Nos. 6,570,468 and 6,600,389 areperformed before the resonator is packaged. But typically, resonatorsmust be operated under high vacuum conditions. To the extent that thetechniques described in U.S. Pat. Nos. 6,570,468 and 6,600,389 are notperformed under high-vacuum—the environment of a packagedresonator—there will be uncertainty as to the amount of frequencytrimming that is required.

Furthermore, it is known that the resonator packaging itself can affectthe resonance frequency of a resonator (see, e.g., Lin et al. at p.293). In other words, the resonance frequency of a resonator can differbefore and after encapsulation in a package. Since the first and secondtechniques discussed above and described in U.S. Pat. Nos. 6,570,468 and6,600,389 are conducted before the resonator is packaged, there is,again, uncertainty as to how much frequency trimming is required.

In a third approach, which is referred to by its inventors as “localizedannealing” or “filament annealing,” the resonator is trimmed after it ispackaged. According to this approach, voltage pulses are applied to theresonator. This causes filament-like heating of portions of theresonator, which results in frequency trimming and improvements in Q.See, Wang et al., “Frequency Trimming and Q-Factor Enhancement ofMicromechanical Resonators Via Localized Filament Annealing,” Dig. Tech.Papers, v(1), 1997 Int'l Conf. Solid-State Sensors and Actuators,Chicago, Ill., pp. 109-112 (Jun. 16-19, 1997).

While the third technique avoids the drawback of the first twoapproaches (i.e., trimming before packaging), it has some otherdeficiencies. In particular, the degree of trim control and Q control isvery dependent upon the method used to dope the resonators in additionto other process-related variations.

As a consequence, there is a need for a method for trimming theresonance frequency of MEMS resonators that avoids at least some of theproblems of the prior art.

SUMMARY

An illustrative embodiment of the present invention is a method formodifying (i.e., trimming) the resonance frequency of a micro-mechanicalresonator. The method avoids at least some of the drawbacks of the priorart.

In accordance with the illustrative embodiment, a packaged resonator istrimmed by directing electromagnetic energy to the resonator through atransparent portion of the resonator package. The energy removes (e.g.,ablates, etc.) mass at the point(s) of contact on the resonator.Removing mass from the resonator affects its resonance frequency in apredictable manner. In some embodiments, the electromagnetic energy issourced from a femtosecond laser.

In some variations of the method, debris that is generated during massremoval is electrostatically attracted to a remote region of thepackage, away from the resonator.

In some further variations of the illustrative embodiment, frequencytrimming is a function of (1) the amount of mass removed from theresonator and (2) the location(s) on the resonator at which the mass isremoved. That is, once the frequency-trimming requirement is determined(i.e., how much change in resonance frequency is required), the trimmingis implemented by removing mass from selected locations on theresonator, since the change in frequency caused by removing mass is notonly a function of the amount of mass, but also its location on theresonant element. In some embodiments, a mass-trimming map is developedor otherwise utilized. The map identifies a plurality of potentialmass-trimming sites on the resonator. Each site can be classified as a“fine-tuning” site or a “coarse-tuning” site as a function of themagnitude of the change in resonance frequency that is caused byremoving (a given amount of) mass at that site. Fine-tuning sites andcoarse tuning sites tend to group in different regions on the resonatoras a function of the aforementioned relationship between resonancefrequency and mass location.

Based on a differential between the measured and desired resonancefrequency of the resonator, and expressions that relate resonancefrequency to location-dependent mass (among other parameters), some ofthe (potential) sites on the map are selected as (actual) sites on theresonator for mass removal.

Also described are embodiments of a packaged micro-mechanical resonatorsuitable for frequency trimming in accordance with the illustrativemethod. In accordance with an illustrative embodiment, at least aportion of the package is transparent to the electromagnetic energy thatwill be used to trim the resonator.

The package encapsulates the resonator in a substantially pressure-tightcavity and advantageously maintains it under vacuum. In someembodiments, electrodes, which are contained within the cavity, can bebiased to a voltage that is suitable for attracting debris that isgenerated during the trimming operation.

Some embodiments of micro-mechanical resonators that have been trimmedin accordance with the method will have a plurality of divots in thesurface thereof. The divots result from mass removal during trimmingoperations. In some variations, the divots will be located symmetricallyon the resonator surface. This symmetric arrangement has the effect ofchanging the resonance frequency while the quality factor, Q, of theresonator remains substantially unaffected. In some other variations,the divots will be asymmetrically located. This asymmetric arrangementresults in a change in both the resonance frequency and the qualityfactor of the resonator.

For reasons previously discussed, it is advantageous (but not necessary)to perform the method on a packaged micro-mechanical resonator. In somevariations of the illustrative embodiment, however, the method isperformed before the resonator is packaged.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a flow diagram of a method in accordance with theillustrative embodiment of the present invention.

FIG. 2 depicts a packaged resonator in accordance with the illustrativeembodiment of the present invention.

FIG. 3 depicts a flow diagram of a variation of the method depicted inFIG. 1.

FIG. 4 depicts a flow diagram of an embodiment of the method depicted inFIG. 3.

FIG. 5 depicts a flow diagram of an embodiment of the method depicted inFIG. 4.

FIG. 6 depicts a flow diagram of a variation of the methods depicted inFIGS. 1, 3, and 4.

FIG. 7 depicts a flow diagram of an embodiment of the method depicted inFIG. 4.

FIG. 8 depicts a mass-trimming map in accordance with the illustrativeembodiment of the present invention.

FIG. 9A depicts a symmetric arrangement of sites at which mass isremoved from a resonator.

FIG. 9B depicts an asymmetric arrangement of sites at which mass isremoved from a resonator.

FIG. 10 depicts a method for forming a package in accordance with theillustrative embodiment.

FIG. 11 depicts a package formed from the method of FIG. 10.

DETAILED DESCRIPTION

In this Specification, numerous specific details are disclosed in orderprovide a thorough description and understanding of the illustrativeembodiments of the present invention. Those skilled in the art willrecognize, however, that the invention can be practiced without one ormore of the specific details, or with other variations of theillustrative methods, materials, components, etc. In some instances,well-known structures, materials, or operations are not shown ordescribed in detail to avoid obscuring aspects of the illustrativeembodiments.

It is understood that the various embodiments shown in the Figures areillustrative representations, and are not necessarily drawn to scale.Reference throughout the specification to “one embodiment” or “anembodiment” or “some embodiments” means that a particular feature,structure, material, or characteristic described in connection with theembodiment(s) is included in at least one embodiment of the presentinvention, but not necessarily in all embodiments. Consequently,appearances of the phrases “in one embodiment,” “in an embodiment,” or“in some embodiments” in various places throughout the Specification arenot necessarily referring to the same embodiment. Furthermore, theparticular features, structures, materials, or characteristics can becombined in any suitable manner in one or more embodiments.

FIG. 1 depicts a flow diagram of the salient operations of method 100 inaccordance with the illustrative embodiment of the present invention. Inthe illustrative embodiment, method 100 is used to trim the resonancefrequency of a micro-mechanical resonator. Typically, and for useherein, the prefix “micro” in the term “micro-mechanical” refers todevices that have size between about 100 nanometers to severalmillimeters. It will be recognized, of course, that thesemicro-mechanical devices will often include structures or componentshaving even smaller dimensions (i.e., less than 100 nanometers).

In accordance with operation 102 of method 100, a package for amicro-mechanical resonator is formed. FIG. 2 depicts features of package206, and of micro-mechanical resonator 208 encapsulated thereby, uponwhich method 100 can be practiced.

Packages and packaging methods for micro-mechanical devices, such asresonator 208, are varied and well known in the art. For example,packages can be formed via wafer-to-wafer bonding by means of anodicbonding, thermocompression bonding, low-temperature fusion bonding,solder bonding, or glass-frit bonding. Furthermore, other means forsealing that use direct bonding of materials commonly used in existingsemiconductor processing can also be used. With the exception of a fewfeatures described below, neither the package nor packaging methods aredescribed in detail herein because they are not germane to anunderstanding of the illustrative embodiments of the present invention.For further detail concerning packages and packaging methods for amicro-mechanical resonator, see, e.g., U.S. patent application Ser. No.10/632,165, incorporated by reference herein.

Likewise, a variety of designs for a micro-mechanical resonator, such asmicro-mechanical resonator 208, are known in the art, many of which aresuitable for use in conjunction with the illustrative embodiment of thepresent invention. Consequently, resonator design and operation will notbe described in detail here unless it furthers an understanding of thepresent invention. Additional detail concerning the design and operationof micro-mechanical resonators, see, e.g., U.S. Pat. Nos. 6,249,073 B1,6,169,321, and 5,976,994; Publ. U.S. Pat. Apps. US 2002/0070816 A1 andUS 2003/0051550 A1; Nguyen et al., “Micromachined Devices for WirelessTelecommunications,” Proc. IEEE, v.(86), no. 8, pp. 1756-1768 (Aug1998); Wang et al., “VHF Free-Free Beam High-Q MicromechanicalResonators,” Technical Dig. Int'l IEEE Micro Electro Mechanical SystemsConf., Orlando, Fla., pp. 453-458 (Jan 17-21, 1999); Nguyen et al.,“Frequency-Selective MEMS for Miniaturized Low-Power CommunicationDevice,” IEEE Trans. Microwave Theory Tech., v(47), no. 8, pp. 1486-1503(Aug 1999); Bannon et al., “High Frequency Micromechanical Filters,”IEEE J. Solid-State Cir., v(35), n. 4, pp. 512-526 (April 2000); Nguyenet al., “Transceiver Front-End Architectures Using VibratingMicromechanical Signal Processors,” Dig. Of Papers, Topical Mtg onSilicon Monolithic Integrated Circuits in RF Systems, pp. 23-32 (Sept.12-14, 2001); and Nguyen, “Vibrating RF MEMS for Low Power WirelessCommunications,” Proc. 2000 Int'l. MEMS Workshop (iMEMS '01), Singapore,pp. 21-34 (July 2001). Each of these references is incorporated hereinin its entirety.

As depicted in FIG. 2, micro-mechanical resonator 208, which includesresonant element 210 and supports 212, is disposed on device substrate214. Typically, resonator 208 is formed from a silicon-containingmaterial (e.g., silicon nitride, silicon-on-insulator, silicon carbide,polysilicon, single-crystal silicon), although other materials, such asmetals or compound semiconductors (e.g., gallium arsenide, etc.), cansuitably be used. Micro-mechanical resonator 208 resides within cavity216, which is advantageously kept under vacuum, at a pressure that istypically 10⁻³ milliTorr or less. Cavity 216 is formed by attaching cap218 to substrate 214. In the illustrative embodiment, cap 218 includesridges 220, which abut substrate 214 and serve as a standoff to formcavity 216. The cavity is typically formed under high temperature, as isusually required to bond cap 218 to substrate 214. The temperature canvary substantially (e.g., 300° C. to 1100° C., etc.) as a function ofthe bonding method used. As package 206 cools, a vacuum is created incavity 216.

In the illustrative embodiment, package 206 includes non-evaporatedgetter 222, which is used for maintaining the vacuum level. The decisionto incorporate getter 222 in package 206 is a function of the pressurein cavity 216. That is, as pressure is reduced (i.e., greater vacuum),it is more likely that getter is required to maintain the low pressure.Resonators that are operating at relatively lower frequency require arelatively lower pressure (i.e., greater vacuum) in cavity 216. Forexample, for a resonator operating at 32 KHz, the pressure must bemaintained at about 1 milliTorr. To maintain such a low pressure, getter222 should be used. For a resonator operating at 19 MHz, the pressuremust be maintained at about 10-100 milliTorr. At this relatively higherpressure level, getter 222 might not be required. And for a resonatoroperating at 1 GHz, the pressure should be maintained at about 1-10Torr. At this yet higher pressure level, getter 222 is typically notrequired. Therefore, the lower the operating frequency of resonator 208,the more likely it is that getter 222 is required.

In operation 204 of method 100, electromagnetic energy 224 is directedfrom EM source 226 through package 206 toward micro-mechanical resonator208. Contact between resonator 208 and electromagnetic energy 224 causesthe removal of a small amount of mass of resonator 208 at the point ofcontact. In accordance with the illustrative embodiment, the point ofcontact will be somewhere on resonant element 210. Removal of the masscreates divot 231 in resonant element 210.

In accordance with the illustrative embodiment, a femtosecond laser isused as EM source 226. Electromagnetic energy 224 from a femtosecondlaser ablates (i.e., creates a plasma) mass from resonator 208. It isadvantageous (but not necessary) to use a femtosecond laser as the EMsource because it causes very little heating beyond the point ofcontact. While other EM sources can be used, such as picosecond lasers,heating of resonator 208 beyond the point of contact is likely to occur.Such heating can deleteriously and unpredictably affect the performanceof resonator 208. As described in more detail later in thisspecification, electromagnetic energy 224 delivers an amount of energyin the range of about 10 to about 50 nanojoules to resonator 208.Furthermore, that amount of energy is advantageously delivered toresonator in about 150 femtoseconds or less.

At least a portion of package 206 must be transparent, at the operatingwavelength of EM source 226, so that electromagnetic energy 224 canreach resonator 208.

In the illustrative embodiment, EM source 226 is disposed above cap 218;consequently, at least a portion of cap 218 must be transparent toenergy from this source. In some embodiments, cap 218 is made of amaterial that is optically transparent at the wavelengths of interest.In some other embodiments, a window 219 of suitable material is providedwithin cap 218. The specific choice of material is a mainly a functionof the operating wavelength of EM source 226 and the coefficient ofthermal expansion of the transparent portion. That is, the coefficientof thermal expansion of cap 218, or of window 219 within cap 218, etc.,will advantageously match the coefficient of thermal expansion ofresonator 208 or substrate 214, or both. Methods for forming anoptically-transparent cap are described later in this specification.

In embodiments in which a femtosecond laser is used as EM source 226,cap 218 or the transparent portion thereof can be made of Pyrex™ orfused silica. When using a femtosecond laser to trim, a “beam focusangle” of up to 25 degrees (included angle) is advantageously used. Asused herein, the term “beam focus angle,” the specified range, and theterm “included angle,” means that electromagnetic energy 224 should bedirected toward resonator 208 focusing to a spot that is approximately0.25 microns to 1 micron in diameter (and more typically about 0.5 toabout 0.7 microns in diameter) and at an angle that is no more thanabout 12.5° with respect to an axis that is normal to the upper surfaceof resonant element 210.

When electromagnetic energy 224 contacts resonator 208, rapid heating ofthe resonator at the point of contact produces a plasma cloud of ionizedmaterials (e.g, atoms and ions) and other small particles, hereinafter“debris.” As described in further detail later in this specification, itis desirable to generate mostly plasma. The reason for this is that thecharged debris that is generated disperses over a wide area withincavity 216. Often, the debris re-deposits on resonator 208 andsurrounding surfaces. This creates a- risk of degraded performance. Inparticular, the debris generated from trimming can become trappedbetween resonant element 210 and underlying substrate 214. This caninterfere with unfettered movement of resonator 208. Furthermore, ifdebris that has settled within cavity 216 later moves to anotherposition on or off of resonator 208, the resonance characteristics ofthe resonator will change.

In accordance with some embodiments of a method in accordance with thepresent invention (see, e.g., FIG. 6: method 600, operation 626), debristhat is formed during mass removal is electrostatically attracted to alocation that is relatively distant from resonator 208, yet still withincavity 216. To this end, in some embodiments, package 206 includeselectrodes 228A and 228B. These electrodes are biased, during trimming,to a voltage that is capable of electrostatically attracting the debrisand keeping it away from resonator 208.

The debris tends to remain at the electrodes (after the biasing voltageis withdrawn) due to a surface-charge attraction. Since this behavior isdesirable, it is promoted by fabricating electrodes 228A and 228B sothat they are advantageously free of a surface passivation layer. Asurface passivation layer is usually applied to MEMS structures toprevent particles from sticking, among other reasons. If present, thepassivation layers would hinder the retention of debris.

Selective passivation of MEMs structures, whereby electrodes 228A and228B are left untreated, can be accomplished by means such as protectingthe electrodes (with an added layer, etc.) to prevent deposition ofpassivation layers or by selectively heating the electrodes afterdeposition to remove the passivation layers.

Furthermore, in some embodiments, narrow features 230 can be formed(e.g., photo-lithographically patterned, etc.) in electrodes 228A and228B to create channels. The channels aid in trapping the debris inconjunction with the surface-charge attraction.

FIG. 3 depicts a flow diagram of the salient operations of method 300,which is a variation of method 100. Operation 306 of method 300 requiresidentifying at least one site on a packaged micro-mechanical resonatorat which mass will be removed. Removal of mass at that site decreases adifference between the actual (i.e., measured) resonance frequency of aresonator (e.g., resonator 208) and the targeted or desired resonancefrequency of the resonator. In accordance with operation 308,electromagnetic energy is directed to the site on the resonator throughthe package.

As mentioned in the Background section of this Specification, it isdesirable to trim the resonance frequency of a resonator after it hasbeen packaged. This is advantageous (but not required) because thepackage itself, as well as the presence of a vacuum, affects theresonance frequency of a resonator.

In some embodiments, operation 306 includes sub-operations 410 and 412,which are depicted in FIG. 4. Sub-operation 410 requires determining anamount of change desired in the resonance frequency of a packagedmicro-mechanical resonator. In some embodiments, sub-operation 410includes sub-operations 514 and 516, which are depicted via flow diagramin FIG. 5. Sub-operation 514 requires measuring the resonance frequencyof a packaged resonator. In sub-operation 516, the measured resonancefrequency (operation 514) is compared with a desired or target resonancefrequency.

Description of sub-operation 412 is deferred until after the descriptionof method 600, which is yet another variation of method 100. Method 600,which is depicted in FIG. 6, combines some of the operations andsub-operations that were previously described as variations of method100. More particularly, method 600 includes, in some embodiments:

-   -   Operation 618—Forming a package for a micro-mechanical resonator        (see FIG. 1, operation 102).    -   Operation 620—Determining an amount of change desired in a        resonance frequency of the resonator (see FIG. 4, sub-operation        410).    -   Operation 622—Identifying at least one site on the resonator at        which to remove mass to achieve the amount of change desired        (see FIG. 3, operation 306).    -   Operation 624—Directing electromagnetic energy through the        package toward the site on the resonator (see FIG. 3, operation        308).    -   Operation 626—Electrostatically attracting debris resulting from        contact of the electromagnetic energy with the site on the        resonator.

After operation 626, processing continues by repeating operation 620. Ifit is determined, in operation 620, that no further change in resonancefrequency is desired, method 600 ends. Otherwise, processing continueswith operation 622.

Sub-operation 412 is now described. Sub-operation 412 requires adetermination of a total quantity of mass to remove from a resonator tocause a desired amount of change in resonance frequency. Sub-operation412 also specifies that the total quantity of mass to be removed isdetermined as a function of the position of the mass (on the resonator),as well as some other considerations described later in thisspecification.

As described by Wang et al. in “VHF Free-Free Beam High-QMicromechanical Resonators,” J. Microelectromechanical Systems, v(9),no. 3, pp. 350 (Sept 2000), the resonance frequency of amicro-mechanical resonator is a function of the stiffness and the massof its resonant element, among other parameters. And stiffness and massare location dependent. The location dependence derives from thevelocity dependence of these quantities, and thus are functions of theresonance mode shape of the resonant element.

In some embodiments, sub-operation 412 includes sub-operations 728 and730, as depicted in FIG. 7. Sub-operation 728 requires the use of amass-trimming map that identifies a plurality of potential sites on theresonator at which to remove mass. Sub-operation 730 recites selectingsites from the map. These sites map to locations on the resonator atwhich mass will be removed.

With regard to sub-operation 730, Wang et al. can be used to predictresonance frequency as a function of location-dependent mass andstiffness for a “free-free” beam resonator. The “free-free” descriptorrefers to the fact that, by virtue of the location and structure of thesupports for the resonating element (i.e., the beam), the resonatingelement ideally sees zero impedance into its supports and effectivelyoperates as if levitated without any supports. Those skilled in the artcan develop expressions for different resonator structures to predictresonance frequency as a function of location-dependent mass, etc.

With regard to sub-operation 728, FIG. 8 depicts free-free beamresonator 832 having resonant element or beam 834 and supports 836.Mass-trimming map 838 is superimposed on resonator 832. It will beunderstood that map 838 does not actually appear on resonator 832; it issuperimposed or mapped onto beam 834 in FIG. 8 for clarity ofexplanation. For ease of description, map 838 of sites 840 and themapping of those sites onto beam 834 will often not be distinguished. Inother words, in at least some instances, no distinction will be madebetween a region of map 838 and that same region on beam. 834.

Mass-trimming map 838 identifies a plurality of potential sites 840 atwhich to remove mass from beam 834. Removing mass from beam 834 at anyof sites 840 will affect the resonance frequency of resonator 832. Inthe embodiment depicted in FIG. 8, sites 840 are arranged in an arraythat covers the upper surface of beam 834.

In light of earlier disclosure, it will be understood that removing massat one particular site 840 on beam 834 will not, necessarily, cause thesame amount of change in the resonance frequency of beam 834 as removingthe same amount of mass from another site 840.

In fact, as a function of a site's location, sites 840 can becategorized as relatively “fine-tuning” or relatively “coarse-tuning.”For a free-free resonator such as resonator 208, it is convenient toreference sites 840 as a function of their position relative to nodallines 8-8 and the center of beam 834. For a free-free resonator such asresonator 208, fine-tuning sites 842 and 844 are disposed relativelycloser to nodal lines 8-8 while coarse-tuning sites are disposedrelatively further from nodal lines 8-8 and closer to the middle of beam834. Removing mass at fine-tuning sites 842 and 844 results in arelatively smaller change in the resonance frequency of beam 834 ascompared to removing the same amount of mass at coarse-tuning sites 846.

In some embodiments, no potential mass-trimming sites 840 are located inregion 848 along or very near to (within a few microns of) nodal lines8-8. This indicates that mass should not be removed from this region ofresonator 832. The reason for this is to avoid damaging relativelydelicate supports 836, which are coupled to beam 834 along nodal lines8-8.

It will be understood that number of sites 840 depicted in map 838 isrepresentative; the actual number of sites is a function of the size ofresonant element 834, the spacing of sites 840 and the expected divotsize. Furthermore, while the relative locations of sites 840 that areidentified as “fine-tuning” or “coarse tuning” are correct for at leastsome embodiments, it is to be understood that the specific number ofrows that are shown to include fine-tuning sites or coarse-tuning sitesand the specific location of those rows is intended to berepresentative. That is, the designation of three rows of sites 840 toeither side of nodal lines 8-8 as “fine-tuning” sites is strictlyillustrative. It will be appreciated that, to some degree, thedesignations “fine-tuning” and “coarse-tuning” are arbitrary and can beassigned a variety of different ranges. That is, as a function ofapplication specifics, it might be equally appropriate to designate a“fine-tuning” site as a site that can trim the resonance frequency in arange of 0.005% to 0.1%, or 0.01% to 0.1%, or 0.075% to 0.15%, etc.

The spacing of sites 840 and the amount of mass removed from each siteis dependent upon several factors, including the focus limit of EMsource 226 and a desire to limit the amount of debris generated duringmass removal. For example, in embodiments in which EM source 226 is afemtosecond laser, the minimum material removal threshold is an energylevel of approximately 10 nanojoules and the focus limit is about 0.5microns. Furthermore, it is advantageous to limit the energy ofelectromagnetic energy 224 that is delivered to beam 834 to about 50nanojoules to restrict the amount of debris generated during massremoval.

Delivering 10 nanojoules of energy to beam 832 creates a divot or dimplethat is about 250 nanometers wide and about 250 nanometers deep.Delivering 50 nanojoules of energy to beam 834 creates a divot that isabout 1 micron wide and about 1 micron deep. Delivering 35 nanojoules ofenergy, as a desirable average within the specified range, creates adivot in beam 834 that is about 700 nanometers wide and 700 nanometersdeep. Based on these dimensions, each potential mass-trimming site 840on mass-trimming map 838 is spaced from its nearest neighbors by atleast about 1 micron.

For a divot having a size of about 700 nanometers in width and depth,fine-trimming sites provide an ability to trim the resonance frequencyin increments within a range of about 0.01% to about 0.1%, as a functionof position. Coarse-trimming sites provide an ability to trim theresonance frequency in increments within a range of about 0.1% to about5%, as a function of position. In particular, the coarsest trimmingsites (e.g., 5%, etc.) are located near the middle of beam 834.

Fine-trimming sites 842 that are located nearer to ends 850 of beam 834provide a finer degree of control than fine-trimming sites 844 that arelocated nearer to the center of beam 834.

Typically, mass will be removed from beam 834 at only some of the manyavailable locations (i.e., at only some of potential mass-trimming sites840 shown in mass trimming map 838). In some embodiments, the sameamount of mass is removed from each such site.

The method provides an ability to tune the resonance frequency of aresonator while not substantially affecting its quality factor, Q. Thisis done in by selecting a symmetrical arrangement of mass-trimming sites840. An example of this is depicted in FIG. 9A, wherein mass is removedat sites 954 (the selected mass-trimming sites 840), which aresymmetrically arranged with respect to center of mass 952 of beam 834.

The method also provides an ability to tune both the resonance frequencyand the quality factor of a resonator. This is done by selecting anasymmetric arrangement of mass-trimming sites 840. An example of this isdepicted in FIG. 9B, wherein mass is removed at sites 954, which areasymmetrically arranged with respect to center 952 of beam 834.

It is expected that as the technical capabilities of EM sources 226improve, divots having a size of about 150 nanometers in width and depthcan repeatedly and accurately be formed. And, naturally, the ability tocreate a relatively smaller divot will equate to a relatively finertuning capability for the method.

Furthermore, a finer tuning capability can be provided by selectivelyusing electrodes 238A and 238B (FIG. 2). As previously described, whenbiased, these electrodes generate an electrostatic force that attractsdebris that is formed during mass removal. To the extent that theelectrodes are deactivated during the process of mass removal, some masswill redeposit on beam 834. This provides, effectively, an ability toremove less mass than might otherwise be possible, the result of whichis a smaller change in resonance frequency. It will be appreciated,however, that some degree of control over the process is sacrificed whenusing this technique.

Sub-operation 730, which requires selecting sites at which to removemass, can be carried out in a variety of ways. For example, in someembodiments, an algorithm can be used to select a group of sites thatshould, after mass removal, fully trim the resonator to bring the actualresonance frequency in line with the desired resonance frequency. Thealgorithm is advantageously based on a correlation between the desiredresonance frequency and parameters that affect the resonance frequency,such as spring constant, total resonator mass, and the resonatorgeometry. See, e.g., Wang et al. in “VHF Free-Free Beam High-QMicromechanical Resonators,” J. Microelectromechanical Systems, v(9),no. 3, pp. 350 (Sept 2000), describing the correlation between resonancefrequency and certain parameters. In some embodiments, finite-elementmodeling, known to those skilled in the art, is used to determine atwhich locations to remove mass and how much mass to remove at thoselocations.

Alternatively, in some other embodiments, a more iterative process canbe employed. In particular, after measuring resonance frequency, masscan be removed at one or more coarse-tuning sites. After removing massat selected coarse-tuning sites, the resonance frequency is re-checked.If the differential between the actual and desired resonance frequencyis reduced to an appropriate amount, additional mass is then removed atfine-tuning sites, and so forth. In some embodiments, the algorithmselects sites so that mass is removed at a minimum number of sites.

It was mentioned earlier that at least a portion of package 206 must betransparent, at the operating wavelength of EM source 226, so thatelectromagnetic energy 224 can reach resonator 208 (see, e.g., FIG. 2).The glass cap must be smooth and distortion free to enable focused lasertransmission through the glass, as is required in the laser trimmingoperation. The glass cannot be etched, because etch methods typicallydull or pattern the glass, such that focused laser transmission wouldnot be possible. FIG. 10 depicts an illustrative embodiment of method1000 for forming an optically-transparent cap and FIG. 11 depictspackage 206 that includes optically-transparent cap 1166.

In accordance with operation 1056 of method 1000, a positive image ofthe physical profile of the desired optically-transparent cap is createdon a silicon wafer (“forming tool”). The structure of the image can bevisualized from optically-transparent cap 1166 depicted in FIG. 11. Inparticular, the positive image would be the “negative” of the surface ofcap 1166 that faces device wafer 214 (that includes MEMS device 208).The positive image can be created by deposition, isotropic etching,anisotropic etching, and/or surface micromachining in known fashion. Asper operation 1058, a wafer comprising an optically-transparentmaterial, such as a blank glass (e.g., Pyrex™, etc.) wafer, is laid overthe image on the forming tool. The wafer is pushed into the positivefeatures on the forming tool, as indicated in operation 1060. Toaccomplish this, in some embodiments, the wafer and forming tool areinserted into a conventional wafer bonder. The wafer bonder is operatedat temperatures just above the softening point of the wafer ofoptically-transparent material as pressure is applied to it and theforming tool. The wafer and the forming tool are then cooled to roomtemperatures. As per operation 1062, the forming tool is removed fromthe wafer (newly-formed cap) by a process, such as a selective chemicaletch, that does not substantially affect the wafer.

In a variation of method 1000, a surface layer of silicon nitride isformed as a coating on the forming tool. It is advantageously added tothe entire silicon surface that contacts the optically-transparentmaterial. In some embodiments, the positive image of the desiredoptically-transparent cap can be formed directly on the silicon nitride.In some other embodiments, the positive image is formed on the siliconsurface of the forming tool, and then silicon nitride is conformallydeposited. The profile of the silicon nitride surface mirrors thepositive image that was formed on the silicon surface of the formingtool. The wafer of optically-transparent material is then brought intocontact with the silicon nitride, rather than the silicon surface of theforming tool. The bonding is done in the presence of an inert gas (e.g.,nitrogen, argon, etc.). Relief angles are advantageously added to thevertical features of forming tool.

When the cap is formed without a nitride coating and without an inertgas atmosphere, glass and silicon will bond, requiring a chemical etchfor separation, as described above. The presence of the silicon nitrideand an inert atmosphere substantially prevents oxide bonding betweenglass and the silicon forming tool.

Once formed, the cap can be used to create MEMS package 206 viawafer-level-packaging. In other words, the package is formed byattaching device wafer 214 and optically-transparent cap 1166 to oneanother, as per operation 1064. Processes suitable for creating awafer-to-wafer bond between cap 1166 and device wafer 214 include,without limitation, anodic bonding, thermocompression bonding,low-temperature fusion bonding, solder bonding, and glass-frit bonding.Alternatively, other ways to hermetically seal the cap on a devicewafer, such as those employing direct bonding of materials commonly usedin existing semiconductor processing can also be used. Any of thesewafer-level joining/sealing processes can be used to join the glass capto a device wafer to create a package. In package 206 depicted in FIG.11, standoffs 1168 create moat 1170 that receives glass frit or solder1172, which creates the hermetic seal after bonding/attachment.

It is to be understood that the above-described embodiments are merelyillustrative of the present invention and that many variations of theabove-described embodiments can be devised by those skilled in the artwithout departing from the scope of the invention. For example, in theembodiments described herein, fine-tuning sites and coarse-tuning sitesare conveniently defined as a function of the position of those siteswith respect to nodal lines. In other embodiments, and in particular forother resonator structures, the fine-tuning sites and coarse-tuningsites can be referenced to some other feature or site on the resonator,as appropriate. It is therefore intended that such variations beincluded within the scope of the following claims and their equivalents.

1. A method comprising: forming a package for a micro-mechanicalresonator, wherein at least a portion of said package is transparent toa first range of wavelengths of electromagnetic radiation; and directingelectromagnetic radiation through said transparent portion of saidpackage toward said micro-mechanical resonator, wherein saidelectromagnetic radiation has at least one wavelength that is withinsaid first range.
 2. The method of claim 1 wherein said electromagneticradiation is directed through said transparent portion of said packagefor a first period of time, wherein said first period of time issufficient to remove mass from said micro-mechanical resonator at afirst site, while not substantially heating said micro-mechanicalresonator, other than at said first site.
 3. The method of claim 1further comprising determining a first resonance frequency of saidmicro-mechanical resonator, wherein said first resonance frequency isdetermined after said package is formed and before said electromagneticradiation is directed through said package.
 4. The method of claim 3further comprising determining a second resonance frequency of saidmicro-mechanical resonator, wherein said second resonance frequency isdetermined after said electromagnetic radiation is directed through saidpackage.
 5. The method of claim 2 wherein directing electromagneticradiation further comprises illuminating said first site using afemtosecond laser.
 6. The method of claim 1 wherein said electromagneticradiation is directed through said transparent portion of said packagefor a first period of time, and wherein an amount of energy delivered insaid first period time by said electromagnetic radiation to saidmicro-mechanical resonator is in a range of about 10 to 50 nanojoules.7. The method of claim 1 wherein said electromagnetic radiation isdirected through said transparent portion of said package for a firstperiod of time, and wherein said first period of time is about 150femtoseconds or less.
 8. The method of claim 1 wherein said first rangeof wavelengths comprises infrared wavelengths.
 9. The method of claim 1wherein forming a package further comprises forming a cavity, whereinsaid cavity is defined by said package, and wherein saidmicro-mechanical resonator is disposed in said cavity, and furtherwherein a pressure in said cavity is less than atmospheric pressure. 10.The method of claim 3 wherein directing electromagnetic radiationfurther comprises removing mass at a plurality of sites on saidmicro-mechanical resonator.
 11. The method of claim 10 wherein asubstantially equal amount of mass is removed from each of saidplurality of sites.
 12. The method of claim 10 wherein said plurality ofsites are characterized as belonging to at least one of either a firstregion and a second region, wherein: said first region is proximal to anodal line of said micro-mechanical resonator; and said second region isdistal to said nodal line; and wherein the method further comprisesselecting said plurality of sites from at least one of said first regionand said second region, as a function of a desired amount of change in aresonance frequency of said micro-mechanical resonator, wherein saiddesired amount of change is a difference between said first resonancefrequency and a desired resonance frequency of said micro-mechanicalresonator.
 13. The method of claim 12 wherein a substantially equalamount of mass is removed at each of said plurality of locations. 14.The method of claim 1 wherein said removed mass comprises debris andgas, the method further comprising electrostatically attracting saiddebris.
 15. The method of claim 1 wherein directing electromagneticradiation further comprises ablating mass from said micro-mechanicalresonator at said first location.
 16. The method of claim 1 whereinforming a package further comprises forming an optically-transparentcap.
 17. The method of claim 16 wherein forming a package furthercomprises attaching said optically-transparent cap and a device wafer toone another, wherein said device wafer includes said micromechanicalresonator.
 18. The method of claim 16 wherein forming anoptically-transparent cap further comprises contacting a wafercomprising an optically-transparent material with a forming tool,wherein said forming tool includes a positive image of a structure ofsaid optically-transparent cap.
 19. The method of claim 18 wherein saidforming tool comprises a layer of silicon nitride, and saidoptically-transparent material contacts said silicon nitride. 20-58.(canceled)
 59. A method comprising: forming a forming tool, wherein saidforming tool comprises an positive image of a structure of a cap for awafer-level package; contacting a wafer and said forming tool, whereinsaid wafer comprises an optically transparent material; and reproducing,in said wafer, a negative of said positive image.
 60. The method ofclaim 59 wherein forming a forming tool comprises depositing a layer ofsilicon nitride on said positive image.
 61. The method of claim 59wherein reproducing comprises: heating said master and said wafer; andapplying pressure so that said positive image of said master is formed,in reverse, on said wafer; thereby forming said cap.
 62. The method ofclaim 61 wherein heating occurs under an inert atmosphere.
 63. Themethod of claim 61 wherein said cap is bonded to a device wafer, whereinsaid device wafer includes a micromechanical device.